Summary: In [J. Nonlinear Sci. 7, 475–502 (1997; Zbl 0903.58020
)] J. M. Ball
defined a generalised semiflow as a means to consider the solutions of equations without (or not known to possess) the property of uniqueness. In particular he used this to show that the 3D Navier-Stokes equations have a global attractor provided that all weak solutions are continuous from
. In this paper we adapt his framework to treat stochastic equations: we introduce a notion of a stochastic generalised semiflow, and then show a similar result to Ball’s concerning the attractor of the stochastic 3D Navier-Stokes equations with additive white noise.